Pythagorean Theorem Flashcards
What is Pythagoras Theorem
a^2 + b^2 = c^2, which is representative of the side lengths of right triangles, was known to earlier civilizations including Babylonians as shown on plimton 322,
how does plimton 322 show pythagorean triples
shows the numbers for c^2 - a^2 with the largest being c = 18541 and a = 12709
what was the Pythagoreans slogan/philosphy
“All is number” which refers to the idea that everything observable can be represented numerically which they demonstrated by showing the mathematics behind musical intervals and scales
What was the disaster found by pythagoreans
the fact that not all lengths can be expressed in rational numbers
When was a solid theory for real numbers finished
not until 1860’s by R. Dedekind
What was on the doorstep of Platos Academy
“Those who don’t know geometry may not enter”
What is Fermat’s last theorem
a^n + b^n = c^n has no integer solutions for n >= 3, this was proved by Wiles fairly recently
